Boundary behavior for the solutions to Dirichlet problems involving the infinity-Laplacian

In this paper, by constructing suitable comparison functions, we mainly analyze the exact boundary behavior for the unique solution near the boundary to the singular Dirichlet problem −Δ∞u=b(x)g(u)−Δ∞u=b(x)g(u), u>0u>0, x∈Ωx∈Ω, u|∂Ω=0u|∂Ω=0, where Ω   is a bounded domain with smooth boundary in RNRN, g∈C1((0,∞),(0,∞))g∈C1((0,∞),(0,∞)), g   is decreasing on (0,∞)(0,∞) with lims→0+⁡g(s)=∞lims→0+⁡g(s)=∞, g is normalized regularly varying at zero with index −γ   (γ>1γ>1) and b∈C(Ω¯) which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary.